Nelson Pinto-Neto, Arthur Scardua

It is widely known that bouncing models with a dust hydrodynamical fluid satisfying ${c_s^2=p_d/\rho_d\approx 0}$, where $c_s, p_d, \rho_d$ are the sound velocity, pressure and energy density of the dust fluid, respectively, have almost scale invariant spectrum of scalar perturbations and negligible primordial gravitational waves. We investigate whether adding another fluid with $1/3 < \lambda = p/\rho < 1$, which should dominate near the bounce, can increase the amplitude of gravitational waves in the high frequency regime, turning them detectable in near future observations for such range of frequencies. Indeed, we show that the energy density of primordial gravitational waves is proportional to $k^{2(9\lambda-1)/(1+3\lambda)}$ for wavelengths which become bigger than the Hubble radius when this extra fluid dominates the background. Hence, as $\lambda \to 1$ (an almost stiff matter fluid), the energy density of primordial gravitational waves will increase faster in frequency, turning them potentially detectable at high frequencies. However, there is an extra factor $I_q(\lambda)$ in the amplitude which decreases exponentially with $\lambda$. The net effect of these two contributions turns the energy density of primordial gravitational waves not sufficiently big at high frequencies in order to be detected by present day or near future observations for models which satisfy the nucleosynthesis bounds and is symmetric with respect to the bounce. Hence, symmetric bouncing models where the background is dominated by a dust hydrodynamical fluid with small sound velocity, do not present any significant amount of primordial gravitational waves at any frequency range compatible with observations, even if there are other fields present in the model dominating the bounce phase. Any detection of such waves will then rule out this kind of models.

Hayato Shimabukuro, Benoit Semelin

The 21 cm signal from the Epoch of Reionization should be observed within the next decade. While a simple statistical detection is expected with SKA pathfinders, the SKA will hopefully produce a full 3D mapping of the signal. To extract from the observed data constraints on the parameters describing the underlying astrophysical processes, inversion methods must be developed. For example, the Markov Chain Monte Carlo method has been successfully applied. Here we test another possible inversion method: artificial neural networks (ANN). We produce a training set which consists of 70 individual sample. Each sample is made of the 21 cm power spectrum at different redshifts produced with the 21cmFast code plus the value of three parameters used in the semi-numerical simulations that describe astrophysical processes. Using this set we train the network to minimize the error between the parameter values it produces as an output and the true values. We explore the impact of the architecture of the network on the quality of the training. Then we test the trained network on the new set of 54 test samples with different values of the parameters. We find that the quality of the parameter reconstruction depends on the sensitivity of the power spectrum to the different parameters at a given redshift, that including thermal noise and sample variance decreases the quality of the reconstruction and that using the power spectrum at several redshifts as an input to the ANN improves the quality of the reconstruction. We conclude that ANNs are a viable inversion method whose main strength is that they require a sparse exploration of the parameter space and thus should be usable with full numerical simulations.

Clifford Cheung, Karol Kampf, Jiri Novotny, Chia-Hsien Shen, Jaroslav Trnka

We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d<6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.

J.D. Bilbao-Ahedo, R.B. Barreiro, D. Herranz, P. Vielva, E. Martínez-González

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.

P. Daniel Meerburg, Joel Meyers, Kendrick M. Smith, Alexander van Engelen

The Thomson optical depth from reionization is a limiting factor in measuring the amplitude of primordial fluctuations, and hence in measuring physics that affects the low-redshift amplitude, such as the neutrino masses. Current constraints on the optical depth, based on directly measuring large-scale cosmic microwave background (CMB) polarization, are challenging due to foregrounds and systematic effects. Here, we consider an indirect measurement of large-scale polarization, using observed maps of small-scale polarization together with maps of fields that distort the CMB, such as CMB lensing and patchy reionization. We find that very futuristic CMB surveys will be able to reconstruct large-scale polarization, and thus the mean optical depth, using only measurements on small scales.

Özenç Güngör, Bryan W. Lynn, Glenn D. Starkman

The weak-scale $U(1)_Y$ Abelian Higgs Model (AHM) is the spontaneous-symmetry-breaking (SSB) gauge theory of a complex scalar $\phi$ and a vector $A^\mu$. In Lorenz gauge, the SSB AHM has: a massless pseudo-scalar $\pi$; a conserved (up to gauge-fixing terms) $U(1)_Y$ global physical current; no conserved $U(1)_Y$ charge; and a Goldstone Theorem, where $\tilde \pi$ in the Kibble representation becomes a true massless Nambu-Goldstone boson (NGB). Two towers of "1-soft-pion" SSB global WTI govern the $\phi$-sector. The 1$^{st}$ tower gives relations among connected off-shell Green's functions, and powerful constraints on the all-loop-orders $\phi$-sector effective AHM Lagrangian. The 2$^{nd}$ tower, governing on-shell connected T-matrix elements, further severely constrains the physics. It guarantees IR finiteness for zero NGB mass; includes the Lee-Stora-Symanzik (LSS) Theorem, forcing the on-shell T-matrix element with only two external pseudoscalar legs to vanish; and is the source of an additional NGB global shift symmetry. Using the Green's functions and the LSS Theorem of the theory, we construct the manifestly symmetric quantum effective potential of the scalar sector of the Goldstone mode of the AHM, in the Lorenz gauge, to all orders in quantum loops. To do so, we solve the Ward Takahashi identities of the theory recursively, and express arbitrary $\phi$-sector Green's functions in terms of those with no external scalar legs and an even number of pseudoscalar legs. The resulting expression for the effective potential is much easier to evaluate at a given order in quantum loops, since many fewer diagrams need be computed for a given number of external $\phi$ legs. In the Kibble representation, the so-constructed effective scalar potential is gauge-independent.